A 1k spiritual beast exp is an item in Evony TKR (The King's Return). It can be found after killing certain monsters or bosses, with some of them listed below.
The description of 1K Spiritual Beast EXP in Evony TKR says:
Use it to gain 1,000 Spiritual Beast EXP for any Spiritual Beast.
1K Spiritual Beast EXP is known to drop from a number of bosses or monsters upon killing, including Werewolf and Manticore.
Note: This list may be incomplete.